Midway through the first half, the Chiefs messed up twice within a minute on the La Rochelle try-line as first Moray Low knocked on as he stretched to go over and then Matt Jess was tackled into touch as he motored towards the right corner.

Exeter's cross-Channel woes

Dec 2013: Lost 32-20 at Toulon (Heineken Cup group stage)

Jan 2013: Lost 46-3 at Clermont Auvergne (Heineken Cup group stage)

Apr 2012: Lost 22-17 at Stade Français (Amlin Cup quarter-final)

Nov 2011: Lost 15-12 at Perpignan (Amlin Cup group stage)

Jan 2011: Lost 32-30 at Montpellier (Amlin Cup group stage)

Oct 2010: Won 34-19 at Bourgoin (Amlin Cup group stage)

Sturgess then had a try disallowed after Ryan Caldwell knocked the ball forward from the resulting lineout.

But the break came five minutes later as McGuigan burst through and ran 50 metres before offloading to Lees, who in turn fed James to go over.

Three minutes later, Exeter got their second try as Sturgess dived in under the posts after a great offload from Kai Horstmann,

However, Exeter were caught napping five minutes before the end as LeBail chipped a perfectly weighted ball into a vacant area behind the Exeter line for Barraque to run on to and score the home side's only try.

Audy's penalty early in the second half was the final time La Rochelle troubled their scorers as Steenson kicked three more penalties to pull Exeter clear.

The hosts had Kaulashvili yellow-carded with nine minutes left after an infringement in the maul and Exeter took advantage to secure the bonus.